Dollar General Corp., the biggest dollar-store chain in the U.S., on Monday offered to pay $9 billion in cash for the second-biggest, Family Dollar Stores Inc., the latest in a wave of retail mergers that comes as companies struggle with weak traffic and a glut of stores.

The offer is an attempt to elbow out the smallest of the three rivals, Dollar Tree Inc., which signed an agreement to acquire Family Dollar three weeks ago. Family Dollar's board said on Monday that it would review the new $78.50-a-share offer, but...